Object being distorted when fixing lighting
When dealing with sculpting it's very important to check whether your model doesn't have any flipped normals before adding Multires modifier (if you flip them after subdivided and sculpted, recalculating shouldn't make any problems. But making any changes in Edit mode on the sculpted model anyway will make you some distortions). You still can recalculate them at any time, but that will result in a mess you see in your case (or even worse).

There are several ways possible taking into account that sculpting must be saved:

Smoothing faces with flipped normals


Enter Edit mode of the corrupted object, select faces with flipped normals and assign them to temporar Vertex Group.
Add Smooth modifier to this object, set created vertex group in the Vertex Group option of the modifier to make it influence only on it.
Set the Repeat value to something high, like 30 or 50, so to make messy vertices return to their place.
Recalculate flipped normals using Ctrl+N.


The Smooth modifier will let you make those faces / vertices stop being distorted and moved far away, at the same time the original sculpting in other areas will be preserved.



This way has disadvantages, of course:


if there are a lot of faces with flipped normals it won't really help you - nearly all faces will be added to group smoothed by the Smooth modifier and that will be the same as just using Smooth brush in Sculpt mode or recreating from scratch all the sculpt.


Leaving inverted normals

It's pretty straightforward - the inverted normals are left as they are, and you continue sculpting, including them if needed. You'll need to recalculate normals after applying Multires modifier (and probably make some adjustments even then).

The trick here will be that as the normals are flipped, the brushes will behave in the opposite way, so on these faces you'll need to use Subtract mode of any brush.



The disadvantages:


It may be quite complex to create any smooth transitions on the areas where flipped / unflipped faces meet as brush may act somewhat unpredictably. 


Smoothing in Sculpt mode

It should be possible to see messed vertices while in Sculpt mode (but I managed once to see them only while in Object mode), and it's possible to smooth them using Smooth brush (press S while in Sculpt mode). Probably it won't be easy to smoothen with brush exactly tjose distorted areas, but it may be worth trying if there isn't big amount of them.



So it's a lot easier to check that there aren't any flipped normals in the model before you add sculpting then to deal with repairing that after and trying to preserve hours of sculpting work.